The resistance \( R \) of a wire can be calculated using the formula:
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.
Since we want to compare the resistances of tungsten and silver wires of the same length and cross-sectional area, we can express their resistances as:
\[ R_{\text{tungsten}} = \rho_{\text{tungsten}} \frac{L}{A} \] \[ R_{\text{silver}} = \rho_{\text{silver}} \frac{L}{A} \]
To find out how many times greater the resistance of the tungsten wire is than that of the silver wire, we can set up the following ratio:
\[ \frac{R_{\text{tungsten}}}{R_{\text{silver}}} = \frac{\rho_{\text{tungsten}}}{\rho_{\text{silver}}} \]
Now, substituting the resistivities given:
- Resistivity of tungsten \( \rho_{\text{tungsten}} = 5.60 \times 10^{-8} , \Omega \cdot m \)
- Resistivity of silver \( \rho_{\text{silver}} = 1.59 \times 10^{-8} , \Omega \cdot m \)
Now we can calculate the ratio:
\[ \frac{R_{\text{tungsten}}}{R_{\text{silver}}} = \frac{5.60 \times 10^{-8}}{1.59 \times 10^{-8}} \]
Calculating this gives:
\[ \frac{5.60}{1.59} \approx 3.52 \]
Thus, the resistance of a tungsten wire is approximately 3.52 times greater than that of a silver wire of the same length and cross-sectional area.
The answer is 3.52.
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